Beyond the Bakushinkii veto: regularising linear inverse problems without knowing the noise distribution

This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinskii veto tells us, that we are not able to solve the equation if we do not know the noise level. But in applications it is...

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Bibliographic Details

Published in:	Numerische Mathematik Vol. 145; no. 3; pp. 581 - 603
Main Authors:	Harrach, Bastian, Jahn, Tim, Potthast, Roland
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2020 Springer Nature B.V
Subjects:	Error analysis Hilbert space Ill posed problems Inverse problems Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Noise levels Numerical Analysis Numerical and Computational Physics Simulation Theoretical 65J22 (Numerical solution to inverse problems in abstract spaces)
ISSN:	0029-599X, 0945-3245
Online Access:	Get full text
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